1. Field of the Invention
The present invention relates to a method of optically measuring a diameter of a single crystal formed using a Czochralski method (hereinafter referred to as the CZ method).
2. Discussion of the Background
One method of producing single crystals used in a semiconductor, for example, is the CZ method. In the CZ method, as shown in FIG. 1, a crucible 2 is filled with a crystal melt liquid 3. The crucible 2 is provided in a furnace body 1 of a CZ furnace. A single crystal 4 is pulled from the melt liquid 3 by a pulling apparatus 5 and is rotated by a rotating apparatus 6. A heater 7 evenly heats the melt liquid 3 by controlling the crucible 2 so that a heating center of the heater 7 and the melt liquid 3 are maintained in a constant positional relationship.
During the pulling operation, a shape of the single crystal 4 should be uniform in both upper and lower end portions, as well as in diameter. This desired shape should be equal to a target value, in both a body and seed crystal portion of the single crystal 4. In addition, a distortion factor defined as a minimum diameter should be equal to or lower than a predetermined minimum value. The distortion factor represents a distortion of a roundness shape of the single crystal 4.
In addition, regarding a quality of the single crystal 4, it is desired to lower a density of an oxidation induced stacking fault (hereinafter referred to as OSF) which is one evaluation item used to determine the quality of the single crystal 4. The OSF represents stacking faults which are caused due to a phenomenon where an oxygen solid solution within the single crystal 4 is precipitated as an oxide in an oxidation treatment of the single crystal 4. The density of the OSF may be reduced by quenching the single crystal 4 as the pulling speed is increased. In addition, increasing the pulling speed of the crystal 4 is beneficial because a production efficiency also increases.
However, when the pulling speed increases, the yield of the single crystal 4 is lowered because the distortion factor increases, thus exceeding the predetermined minimum value. Therefore, it is necessary to set an optimum pulling speed which is within an allowable range to achieve the desired yield, quality, etc., of the single crystal 4. Further, it is important to accurately measure the diameter of the single crystal 4, as well as to calculate an accurate distortion factor.
A first way of measuring the diameter of the single crystal 4 includes calculating the diameter based on a weight of the pulled single crystal 4 (hereinafter referred to as the weight method). Alternatively, the diameter may be measured by using an optical device, such as a one dimensional CCD camera (hereinafter referred to as the optical method).
When the crystal is pulled using the CZ method, as shown in FIG. 3, projections 4a.sub.1, 4a.sub.2, 4a.sub.3, and 4a.sub.4, appear on a peripheral portion of the single crystal 4. The projections 4a.sub.1 -4a.sub.4 are referred to as crystal habit lines, and extend in a crystallographic axis direction. Further, it is important to include the diameter of these crystal habit lines when calculating the distortion factor. However, the weight method calculates an average diameter based on the weight and length of the single crystal 4. Thus, the diameter of the crystal habit lines is not measured. On the contrary, the optical method is able to measure the diameter of the portion of the crystal habit lines, because a diameter of a high brilliant fusion ring created by an interference between the melted liquid 3 and the single crystal 4 may be optically measured.
In the optical method, as shown in FIG. 1, an interface of the single crystal 4 and the melted liquid 3 is optically measured using the one dimensional CCD camera 8 through a window 9 provided in an upper end portion of the furnace body 1. FIG. 2 illustrates that intersecting points C and C' are detected from a change in brilliance between a fusion ring A on the periphery of the single crystal 4 and a light measuring line B-B' of the one dimensional CCD camera 8, so as to measure the diameter of the single crystal 4. In addition, the detection of the intersection points C and C' are continued throughout one rotation of the single crystal 4. An interval W(.alpha.) of the intersection points C and C' is obtained by using the following equation to measure the diameter across the entire periphery of the single crystal 4. EQU W(.alpha.)=L(.alpha.)-R(.alpha.)
L(.alpha.), R(.alpha.): detected positional data of the intersection points C and C' PA1 .alpha.: rotational angle of the single crystal PA1 D: crystal diameter PA1 W: interval between intersection points C and C' PA1 a: distance from crystal center O to light measuring line B-B'
In this case, when the one dimensional CCD camera 8 is provided so that the light measuring line B-B' passes through a center O of the single crystal 4, the fusion ring A may not be brilliant enough which results in diameter measurement errors. Therefore, it is often impossible to measure the diameter of the single crystal 4. Thus, the light measuring line B-B' of the one dimensional CCD camera 8 is positioned on a same side as the camera 8 from the crystal center O (i.e., offset from the center O). In this case, the diameter of the single crystal 4 is measured using the following equation. EQU D=(W.sup.2 +4a.sup.2).sup.1/2
In the conventional optical method, as described above, the distance W of the intersection points C and C' is calculated from the difference between the detected positional data L(.alpha.) and R(.alpha.), i.e., [L(.alpha.)-R(.alpha.)]. When an orientation of the single crystal 4 is [100] as shown in FIG. 3, the crystal habit lines 4a.sub.1, 4a.sub.2, 4a.sub.3, and 4a.sub.4 appear on the outer face of the single crystal 4 at intervals of 90.degree.. If the light measuring line B-B' of the one dimensional CCD camera passes through the center O of the single crystal 4, the two crystal habit lines 4a.sub.1 and 4a.sub.3, for example, simultaneously coincide with the light measuring line B-B'. Therefore, if the fusion ring A was brilliant enough, the diameter of the single crystal 4 including the crystal habit lines 4a.sub.1 and 4a.sub.3 may be measured with comparatively high precision using the difference between the detected positional data L(.alpha.) and R(.alpha.) of the intersection points C and C'.
However, as described above, the light measuring line B-B' is offset from the crystal center O. In this case, the two crystal habit lines 4a, and 4a.sub.3 do not simultaneously coincide with the light measuring line B-B'. That is, when the crystal habit line 4a, coincides with the light measuring line B-B', the crystal habit line 4a.sub.3 does not coincide with this line. The same is true for the crystal habit lines 4a.sub.2 and 4a.sub.4. Thus, in the conventional optical method which obtains the interval W of the intersecting points C and C' from the difference between the detected positional data L(.alpha.) and R(.alpha.), the diameter measuring accuracy is considerably reduced near the crystal habit lines 4a.sub.1, 4a.sub.2, 4a.sub.3 and 4a.sub.4.
In addition, as the crucible rises, an error is caused in a liquid surface position because an accurate liquid phase positional detection method is not used. As a result, the light measuring line B-B' of the one-dimensional CCD camera 8 is deviated from an initially set position. That is, the distance "a" from the crystal center O to the light measuring line B-B' is changed. Thus, this error is included in the measured diameter D.
To solve this problem, the Japanese Patent Application Laid-Open No. 63-256594, discloses a method of moving the light measuring line B-B' of the one-dimensional CCD camera 8 in a direction at a right angle to the line. Then, a diameter value is established using a crystal diameter measured before and after the movement, as well as a moving distance of the light measuring line B-B'. However, this method does not solve the problem that the diameter measuring precision is reduced near the crystal habit lines from the light measuring line B-B' being offset from the crystal center O.
In light of this situation, the present inventor developed (Japanese Patent Application Laid-Open No. 7-282460, which is incorporated herein by reference in its entirety) a single crystal diameter measuring method which includes independently detecting the intersection positions on two sides of the crystal, respectively. This is achieved by detecting the intersection positions on two sides of the crystal from a brilliance change in the intersection points C and C' between the fusion ring A and the light measuring line B-B' of the camera. In addition, a timing difference .theta. corresponding to the intersection point positional changes on the two sides of the crystal is determined by the position of the light measuring line B-B' of the camera and the detected intersection point positional data L(.alpha.) and R(.alpha.). Further, the detected intersection positional data L(.alpha.) and R(.alpha.) is compared, taking into account the timing difference .theta., so as to increase the diameter measuring precision near the crystal habit lines.
In summary, a single crystal formed using the CZ method includes crystal habit lines in a peripheral direction intrinsic to the crystal orientation, as described above. When, for example, the crystal orientation is (100), a crystal habit line occurs every 90.degree.. When a respective crystal habit line crosses the light measuring line B-B' of the one-dimensional CCD camera, the intersection point position between the fusion ring A and the light measuring line B-B' changes.
When the light measuring line B-B' passes the crystal center O, the changes in the intersection point position occur simultaneously. However, when the light measuring line B-B' is separated from the crystal center O, a dispersion results from the timing difference .theta. of the intersection point position. In addition, the timing difference .theta. becomes larger as the distance from the crystal center O to the light measuring line B-B' is increased.
However, the single crystal is also shook, during the pulling operation with a period of four times during one revolution. When the single crystal is shook to the right and left as seen from the one-dimensional CCD camera, the influence of this shaking may be removed by determining the difference of the detected intersection point positional data L(.alpha.) and R(.alpha.). However, when the single crystal is shook longitudinally, the distance from the light measuring line B-B' to the crystal center O changes, which reduces the diameter measuring precision. In addition, the precision of the measuring process is further complicated and reduced because the single crystal is shook at the same time it is pulled and rotated. That is, shaking the single crystal has a large effect on the precision of the diameter measuring process.